Offshore wind: Evidence for two-dimensional turbulence and role of sea horizon

So-Kumneth Sim, Joachim Peinke, Philipp Maass

Published 2022-03-15Version 1

We analyse offshore wind speeds with a high time resolution of one second over a long period of 20 months for different heights above the sea level. Power spectra $S(f)$ show a scaling behaviour consistent with three-dimensional turbulence at high frequencies, followed by the so-called spectral gap region at lower frequencies, where $fS(f)$ varies weakly. For frequencies lower than a crossover frequency $f_{\rm\scriptscriptstyle 2D}$, a rapid rise of $fS(f)$ occurs, which reflects the scaling $fS(f)\sim f^{-2}$ and $fS(f)\sim f^{-2/3}$ of the enstrophy and inverse energy cascade of two-dimensional turbulence. Contrary to earlier observations but in agreement with theoretical predictions, the regime of the enstrophy cascade appears at higher frequencies compared to that of the inverse energy cascade. Strikingly, an analysis of the third moment (structure function) $D_3(\tau)$ of wind speed differences for a given time lag $\tau$ provides strong further evidence of a transition to two-dimensional turbulence. This is reflected in a rapid change from negative to positive values of $D_3(\tau)$ at lags close to $1/f_{\rm\scriptscriptstyle 2D}$. We argue that the physical meaning of $f_{\rm\scriptscriptstyle 2D}$ is connected with the distance of the sea horizon from the measurement point.